Title : Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential

Authors : Ming you Zhang and Md Salik Ahmed*

Abstract : The Cauchy problem of nonlinear Schr¨odinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. By introducing a family of potential wells we not only give some su?cient conditions of global existence and ?nite time blow up of solutions, but also obtain some di?erent sharp conditions for global existence of solution and some invariant sets of solutions.

Journal : Advances in Nonlinear Analysis Volume : 9 Year : 2019 Issue : 1
Pages : 882-894 City : Edition : Editors :
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